Stable Coalition Structure Research Articles

On Myopic Stability Concepts for Hedonic Games

We present a unified look at myopic stability concepts for hedonic games, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and present a sufficient condition for the existence of contractually Nash stable coalition structures on the class of separable games.

Stable Coalition Structures in Simple Games with Veto Control

In this paper we study hedonic coalition formation games in which players' preferences over coalitions are induced by a semi-value of a monotonic simple game with veto control. We consider partitions of the player set in which the winning coalition contains the union of all minimal winning coalitions, and show that each of these partitions belongs to the strict core of the hedonic game. Exactly such coalition structures constitute the strict core when the simple game is symmetric. Provided that the veto player set is not a winning coalition in a symmetric simple game, then the partition containing the grand coalition is the unique strictly core stable coalition structure.

A Note on the Impossibility of a Satisfactory Concept of Stability for Coalition Formation Games

In this note we show that no solution to coalition formation games can satisfy a set of axioms that we propose as reasonable. Our result points out that solutions to the coalition formation cannot be interpreted as predictions of what would be resting points for a game in the way stable coalition structures are usually interpreted.

A note on the impossibility of a satisfactory concept of stability for coalition formation games

We show that no solution to coalition formation games can satisfy a set of axioms that we propose as reasonable. Our result points out that “solutions” to the coalition formation cannot be interpreted as “resting points” in the way stable coalition structures are usually interpreted.

COALITION FORMATION IN A GLOBAL WARMING GAME: HOW THE DESIGN OF PROTOCOLS AFFECTS THE SUCCESS OF ENVIRONMENTAL TREATY‐MAKING

ABSTRACT. We combine new concepts of noncooperative coalition theory with an integrated assessment model on climate change to analyze the impact of different protocol designs on the success of coalition formation. We analyze the role of “single versus multiple coalitions,”“open versus exclusive membership,”“no, weak and strong consensus about membership” and “no transfers versus transfers.” First, we want to find out whether and how modifications of the standard assumptions affect results that are associated with the widely applied cartel formation game in the noncooperative game theoretic analysis of international environmental agreements. Second, we discuss normative policy conclusions that emerge from the various modifications. Third, we confront our results with evidence on past international environmental treaties and derive an agenda for future research.

An Algorithm for Stable and Equitable Coalition Structures with Public Goods

We study the formation of coalitions that provide public goods to members. Individuals are linked on a tree graph and those with similar preferences are connected on the tree. We present a well-defined solution that selects envy-free allocations from the core.

COALITION FORMATION IN GAMES WITHOUT SYNERGIES

This paper establishes sufficient conditions for the existence of a stable coalition structure in the "coalition unanimity" game of coalition formation, first defined by Hart and Kurz (1983) and more recently studied by Yi (1997, 2003). Our conditions are defined on the strategic form game used to derive the payoffs of the game of coalition formation. We show that if no synergies are generated by the formation of coalitions, a stable coalition structure always exists provided that players are symmetric and either the game exhibits strategic complementarity or, if strategies are substitutes, the best reply functions are contractions.

A Taxonomy of Myopic Stability Concepts for Hedonic Games

We present a taxonomy of myopic stability concepts for hedonic games in terms of deviations, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and provide sufficient conditions for the existence of contractually Nash stable and weak individually stable coalition structures on the class of separable games.

Supplier coalitions in on-line reverse auctions: Validity requirements and profit distribution scheme

This paper studies the formation of supplier coalitions in on-line reverse auctions. An auction mechanism with supplier coalitions is proposed, which allows suppliers to form coalitions with one another for the purpose of enhancing their profitability and providing them inventives to participate in on-line reverse auctions. Basic requirements are identified for a valid coalition mechanism, and the requirements include individual rationality, market efficiency compatibility, maintaining competition, observability and controllability, and financial balancedness. The proposed coalition mechanism is well defined and satisfies all validity requirements. The stable coalition structure under this mechanism is also studied, and it is proved that under symmetric information there exists one unique strongly stable coalition structure. The grand coalition usually does not form a strongly stable coalition structure.

Dynamic Coalition Formation in the Apex Game

This paper studies stability of coalition structures in the apex game by the use of Bloch's (1996) model of dynamic coalition formation. In our model, players' payoffs are given by the coalition values and a cost for proposal is newly introduced. We study stable coalition structures by the subgame perfect equilibrium and we show that in the apex game stable coalition structures depend on the cost for making a proposal and who the first proposer is. As opposed to the static analysis by Hart and Kurz (1983), it turns out that the apex may form a two-person coalition with a minor player. Owen (1977) defined the coalition value, that is, a generalized Shapley value (Shapley, 1953) with a priori coalition structure. Hart and Kurz (1983) studied stability of coalition structures using the coalition value. Their models were presented as strategic form games, and the strong Nash equilibrium (Au­ mann, 1967) was used to study stable coalition structures. In particular, they studied stable coalition structures in the apex game, and showed that if the number of the players is greater than or equal to five, the coalition of all minor players is a unique stable coalition. On the other hand, a dynamic process of coalition formation was investigated in Bloch (1996). In this paper, we apply Bloch's dynamic coalition forma­ tion model to the apex game after slightly modifying the model. Players' payoffs are given by the coalition value and costs for making proposals are newly introduced. We use the subgame perfect equilibrium to study stable coalition structures.

Enemies and Friends in Hedonic Games: Individual Deviations, Stability and Manipulation

We consider hedonic games with separable preferences, and explore the existence of stable coalition structures if only individual deviations are allowed.For two natural subdomains of separable preferences, namely preference domains based on (1) aversion to enemies and (2) appreciation of friends, we show that an individually stable coalition structure always exist, and a Nash stable coalition structure exists when mutuality is imposed.Moreover, we show that on the domain of separable preferences a contractual individually stable coalition structure can be obtained in polynomial time.Finally, we prove that, on each of the two subdomains, the corresponding algorithm that we use for finding Nash stable and individually stable coalition structures turns out to be strategy-proof.

Unique stability in simple coalition formation games

We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterization of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterization using a graph representation, explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.

Coalition Formation in a Global Warming Game: How the Design of Protocols Affects the Success of Environmental Treaty-Making

We combine the newest concepts o non-cooperative coalition theory with a computable general equilibrium model close to the seminal RICE-model of Nordhaus and Yang (1996) to determine stable coalition structures in a global warming game. We consider three coalition games that allow for the formation of multiple coalitions. The coalition games represent different designs of climate treaty protocols. Counterintuitively, it turns out that treaties based on a unanimous decision rule and exclusive membership lead to superior outcomes than treaties with open membership. We also demonstrate that if coalition formation is not restricted to a single coalition, as this has been done previously in the literature, coalition structures with multiple coalitions will emerge in equilibrium. Most of the regional agreements are superior to single agreements. Moreover, our findings confirmthose derived fromsim pler theoretical models that a cleverly designed transfer scheme can foster cooperation and that fromthe number of participants the success of a treaty cannot be inferred. They also support a conjecture of theory that in the case of greenhouse gases stable coalition structures (partial cooperation) can close the gap between the global optimum (full cooperation) and the Nash equilibrium(no cooperation) by a substantial amount

A Non-cooperative Foundation of Core-Stability in Positive Externality NTU-Coalition Games

We identify the core as an appealing stability concept of cooperative game theory, but argue that the non-cooperative approach has conceptual advantages in the context of economic problems with externalities. Therefore, we derive a non-cooperative foundation of core-stability for positive externality NTU-games. First, in the spirit of Hart/Kurz (1983), we develop a game that we call - game and show that strong Nash equilibria coalition structures in this game are identical to - and - core stable coalition structures. Second, as a by-product of the definition of the - game, we develop an extension called an - game. Finally, we compare equilibria in the - and - game with those in the - and - game of Hart and Kurz (1983).We identify the core as an appealing stability concept of cooperative game theory, but argue that the non-cooperative approach has conceptual advantages in the context of economic problems with externalities.

Evolutionarily Stable Coalition Structure

We analyze the formation and stability of coalitions for a situation where finitely many individuals form different coalitions and their payoffs depend on the consequence of a noncooperative game with different coalitions, and examine the moving path of individuals among various coalitions. Our main finding is to show that there exists at least one evolutionarily stable coalition equilibrium in Γnx.

Endogenous formation of research coalitions with spillovers

We examine the endogenous formation of research coalitions with high spillovers among symmetric firms. Members of a research coalition set their R and D investments in order to maximize the aggregate profits of members of their coalition. The Exclusive Membership rule supports a more “concentrated” coalition structure and thus leads to higher industry R and D investments for high spillovers than the Open Membership rule does. However, due to free-riding problems, the grand research coalition, which is the socially efficient outcome, is rarely an equilibrium outcome under either rule. Our results suggest that government subsidies to research consortia for basic research with high spillovers can improve social welfare by encouraging wider participation to a research consortium, that is, by alleviating free-rider problems in coalition formation. From a more theoretical viewpoint, our results on stable coalition structures are applicable to a wide variety of economic coalitions with positive externalities.

Stable Coalition Structures with Open Membership and Asymmetric Firms

I study games of coalition formation with open membership where firms form associations in order to decrease their costs before competing on the market. According to previous analyses, only the grand coalition forms at the Nash equilibrium of such games. I show that this result hinges on the assumption of symmetric firms. I therefore introduce asymmetric firms in a game where only two associations can form. I demonstrate that there exists a coalition-proof Nash equilibrium coalition structure in this game, and that when the equilibrium involves two associations, all the members of an association have a higher taste for this association than all nonmembers do. Journal of Economic Literature Classification Numbers: C70, C72, L13.

An algorithm for computing the stable coalition structures in tree-graph communication games

We construct an algorithm which provides in finite steps the stable coalition structure(s) of tree-graph communication games and an allocation of the core: the restricted marginal contribution allocation.

International Games on Climate Change Control

In this paper a n-player non-cooperative game is used to model countries' decision of whether or not to sign an international agreement on climate change control. The stable coalition structure of the game is defined and then computed for a climate game in which the role of carbon leakage is also taken into account. At the equilibrium, a coalition may emerge despite the public good nature of climate. The size of the coalition depends on the degree of interdependence of countries' emission strategies, and on the type of conjectures that each country forms on the consequences of its own decision to join or to defect from the environmental coalition.

Stable Coalition Structures with Externalities

This paper argues that the sign of external effects of coalition formation provides a useful organizing principle in examining economic coalitions. In many interesting economic games, coalition formation creates eithernegativeexternalities orpositiveexternalities for nonmembers. Examples of negative externalities are research coalitions and customs unions. Examples of positive externalities include output cartels and public goods coalitions. I characterize and compare stable coalition structures under the following three rules of coalition formation: the Open Membership game of Yi and Shin (1995), the Coalition Unanimity game of Bloch (1996), and the Equilibrium Binding Agreements of Ray and Vohra (1994).Journal of Economic LiteratureClassification Numbers: C72, C71.